Note the difference from our previous construction [1]}: first of all, this time the input
is the two-dimensional Borchers triple, while we used chiral components in [1]}.
Accordingly, the representation \(\widetilde{T}_{\mathrm {c}}\)  is now just the two copies of the given one. The formula for
\(\widetilde{\mathcal {M}}_{\mathrm {c},\kappa }\)  or \(\widetilde{\mathcal {M}}_{\mathrm {c},k}\)  is also similar, but this time we take both \(x\)  and \(y\)  from the same algebra \(\mathcal {M}_{\mathrm {c}}\) .
